## Geometric Invariant Theory, Volume 34"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants. |

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### Contents

I | 1 |

II | 2 |

III | 4 |

IV | 9 |

V | 13 |

VI | 19 |

VII | 24 |

VIII | 27 |

XXVIII | 115 |

XXX | 120 |

XXXI | 124 |

XXXII | 127 |

XXXIII | 129 |

XXXIV | 138 |

XXXV | 142 |

XXXVI | 144 |

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### Common terms and phrases

abelian scheme abelian varieties action of G affine Algebraic geometry Amer ample base extension Betti numbers canonical Cartier divisor categorical quotient char closed subscheme cohomology compact compactification complex components Corollary defined Definition dimension equivariant finite type follows function functor G acts G-linearization Geom geometric invariant theory geometric points geometric quotient group actions group G hence Hilbert homomorphism induced integers invertible sheaf irreducible isomorphism Kahler Lecture Notes lemma level n structure line bundle linear manifold maximal torus moduli scheme moduli space moment map Moreover morphism noetherian nonsingular Notes in Math open set open subset orbit PGL(n polarization polynomial pre-scheme Proc projective variety Proof proper Proposition prove rational reductive group representation resp result Riemann surface semi-stable sheaves singular SL(n smooth space of curves Spec Springer subgroup subspace suppose surjective symplectic quotient Theorem theta topology valued point vector bundles Yang-Mills